In this paper, we present a new nonintrusive reduced basis method when a cheap low-fidelity model and an expensive high-fidelity model are available. The method employs proper orthogonal decomposition method to generate the high-fidelity reduced basis and a shallow multilayer perceptron to learn the high-fidelity reduced coefficients. In contrast to previously proposed methods, besides the model parameters, we also augmented the features extracted from the data generated by an efficient bi-fidelity surrogate developed in Narayan et al. (SIAM J Sci Comput 36(2):A495–A521, 2014) and Zhu et al. (SIAM/ASA J Uncertain Quantif 2(1):444–463, 2014) as the input feature of the proposed neural network. By incorporating relevant bi-fidelity features, we demonstrate that such an approach can improve the predictive capability and robustness of the neural network via several benchmark examples. Due to its nonintrusive nature, it is also applicable to general parameterized problems.

在本文中，当便宜的低保真模型和昂贵的高保真模型可用时，我们提出了一种新的非侵入式降基方法。该方法采用适当的正交分解方法生成高保真度降低的基础，并采用浅层多层感知器来学习高保真度降低的系数。与先前提出的方法相比，除模型参数外，我们还增强了从Narayan等人开发的有效双保真替代物生成的数据中提取的特征。（SIAM J Sci Comput 36（2）：A495-A521，2014）和Zhu等。（SIAM / ASA J Uncertain Quantif 2（1）：444–463，2014）作为拟议神经网络的输入特征。通过合并相关的双保真功能，我们通过几个基准示例证明了这种方法可以提高神经网络的预测能力和鲁棒性。由于其非侵入性，它也适用于一般参数化问题。